1) Complete problems 10 and 17-18 on pg. 109-111. Use R where possible. Data sets (so you don’t have to type things in) are available at http://www.zoology.ubc.ca/~whitlock/ABD/teaching/datasets.html.

  1. Refer to the previous problem (Practice Problem 9).
  1. Using an approxmiate method, provide a rough 95% confidence interval for the population mean
#Load Libraries
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(readr)
library(ggplot2)
library(forcats)

# Load Dataset
gene_reg <- read_csv("data/04q11NumberGenesRegulated.csv")
## Parsed with column specification:
## cols(
##   ngenes = col_integer(),
##   frequency = col_integer()
## )
# Vectorize Dataset
gene_vec <- rep(gene_reg$ngenes,gene_reg$frequency)

#Visualise Data
ggplot(as.data.frame(gene_vec), aes(x = gene_vec)) + geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# Calculate Mean, Standard Deviation, and Standard Error
f_mean <- mean(gene_vec)
f_sd <- sd(gene_vec)
f_se <- f_sd/sqrt(length(gene_vec))

ci <- c(abs(f_se*2-f_mean),f_se*2+f_mean)

The correct interpretation is that we are confident that the true population mean lies between 6.8652419 and 9.7586113

  1. I think this is the correct interpretation.

# Set up beetles vector
beetles <- c(51, 45, 61, 76, 11, 117, 7, 132, 52, 149)
  1. What is the mean and the standard deviation of beetles per flower?
beetles_mean <- mean(beetles)
beetles_sd <- sd(beetles)

The mean is 70.1 and the standard deviation is 48.5007446.

  1. What is the standard error of the estimate of the mean?
beetles_se <- beetles_sd/sqrt(beetles)

The standard error of the mean is 6.7914627, 7.2300641, 6.209884, 5.563417, 14.6235247, 4.4838954, 18.3315584, 4.221448, 6.7258431, 3.9733358.

  1. Give an apprximate 95% confidence interval of the mean. Provide the lower and upper limits.
beetles_ci <- 2*beetles_se
beetles_CI_low <- beetles_mean - beetles_ci
beetles_CI_high <- beetles_mean + beetles_ci

The lower CI limit is 56.5170747, 55.6398718, 57.680232, 58.9731661, 40.8529506, 61.1322092, 33.4368833, 61.6571041, 56.6483137, 62.1533284 and the standard deviation is 83.6829253, 84.5601282, 82.519768, 81.2268339, 99.3470494, 79.0677908, 106.7631167, 78.5428959, 83.5516863, 78.0466716.

  1. If you had been given 25 data points instead of 10, would you expect the mean to be greater, less than, or about the same as the sample mean?
    same as

  2. If you had been given 25 data points instead of 10, would you expect the standard deviation to be greater, less than, or about the same as the sample standard deviation? greater than

  3. If you had been given 25 data points instead of 10, would you expect the standard error to be greater, less than, or about the same as the sample standard error? less than

2.1) Load the data using readr and make the Month_Names column into a factor whose levels are in order of month using forcats::fct_inorder. Use levels() - a function that takes a factor vector and returns the unique levels - on the column. Are they in the right order?

theme_set(theme_bw(base_size=12))

# Read CSV file 
ice <- read_csv("data/NH_seaice_extent_monthly_1978_2016.csv") %>%
  # Add column with month names
  mutate(Month_Name = factor(Month_Name)) %>%
  # Use fct_inorder to order months
  mutate(Month_Name = fct_inorder(Month_Name))
## Parsed with column specification:
## cols(
##   Year = col_integer(),
##   Month = col_integer(),
##   Day = col_integer(),
##   Extent = col_double(),
##   Missing = col_integer(),
##   Month_Name = col_character()
## )
# Check if months are in order
levels(ice$Month_Name)
##  [1] "Nov" "Dec" "Feb" "Mar" "Jun" "Jul" "Sep" "Oct" "Jan" "Apr" "May"
## [12] "Aug"

__Levels(ice$Month_Name) showed that fct_inorder did not order the months from Jan-Dec.

2.2) Try fct_rev() on ice$Month_Name (I called my data frame ice when I made this). What is the order of factor levels that results? Try out fct_relevel(), and last, fct_recode() as well. Look at the help files to learn more, and in particular try out the examples. Use these to guide how you try each functino out. After trying each of these, mutate month name to get the months in the right order, from January to December. Show that it worked with levels()
Note, if you don’t want a lot of output to be spit out, you can do something like levels(fct_rev(ice$Month_Name)).

levels(fct_rev(ice$Month_Name))
##  [1] "Aug" "May" "Apr" "Jan" "Oct" "Sep" "Jul" "Jun" "Mar" "Feb" "Dec"
## [12] "Nov"
levels(fct_relevel(ice$Month_Name, "Apr","May"))
##  [1] "Apr" "May" "Nov" "Dec" "Feb" "Mar" "Jun" "Jul" "Sep" "Oct" "Jan"
## [12] "Aug"
levels(fct_recode(ice$Month_Name, Month = "Feb"))
##  [1] "Nov"   "Dec"   "Month" "Mar"   "Jun"   "Jul"   "Sep"   "Oct"  
##  [9] "Jan"   "Apr"   "May"   "Aug"
ice <- ice %>%
  mutate(Month_Name = fct_relevel(Month_Name, 
                                  "Jan", "Feb", "Mar", "Apr", "May", "Jun",
                                  "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"))

levels(ice$Month_Name)
##  [1] "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov"
## [12] "Dec"

fct_rev reverses the order of the levels(ice$Month_Name) output fct_relevel() moved April and May to the front of the vector __fct_recode changed the month name “Feb” in the levels vector into “Month”.

2.3) Now, using what you have just learned about forcats, make a column called Season that is a copy of Month_Name. Use the function fct_recode to turn it into a factor vector with the levels Winter, Spring, Summer, Fall in that order. Use levels() on ice$Season to show that it worked.

# Add a column with seasons
ice <- ice %>%
  mutate(Season = fct_recode(Month_Name,
                             Winter = "Jan", Winter = "Feb", Spring = "Mar", Spring = "Apr", 
                             Spring = "May", Summer = "Jun",
                                 Summer = "Jul", Summer ="Aug", 
                             Fall = "Sep",Fall =  "Oct", Fall = "Nov", Winter = "Dec"))

# Check if levels are in order by season
levels(ice$Season)
## [1] "Winter" "Spring" "Summer" "Fall"

2.4) Make a boxplot showing the variability in sea ice extent every month.

p_box <- ggplot(data = ice,
       mapping = aes(x = Month_Name, y = Extent)) + 
       xlab("Month") +
       ylab("Sea Ice Extent") +
  geom_boxplot()

p_box

2.4) Use dplyr to get the annual minimum sea ice extent. Plot minimum ice by year, and add a trendline (either a smooth spline or a straight line).

ice_summary <- ice %>%
  group_by(Year) %>%
  summarize(min_extent = min(Extent))

ggplot(ice_summary,
       aes(x = Year, y = min_extent)) +
  geom_point() +
  ylab("Minimum Sea Ice Extent") + 
  stat_smooth(method = "lm")

2.5) With the original data, plot sea ice by year, with different lines for different months. Then, use facet_wrap and cut_interval(Month, n=4) to split the plot into seasons.

p_seasonal <- ggplot(data = ice,
       mapping = aes(x = Year, y = Extent, group = Month)) +
  geom_line()

p_seasonal + facet_wrap(~cut_interval(Month, n = 4))

2.6) Last, make a line plot of sea ice by month with different lines as different years. Gussy it up with colors by year, a different theme, and whatever other annotations, changes to axes, etc., you think best show the story of this data. For ideas, see the lab.

library(viridis)
## Loading required package: viridisLite
p_annual <- ggplot(data = ice,
       mapping = aes(x = Month_Name, y = Extent, color = Year,
                     group = Year)) +
  geom_line() +
  scale_color_viridis(option = "E") +
  scale_x_discrete(expand=c(0,0))

p_annual

2.7 Extra Credit) Make it animated with gganimate. Just like above. See the lab for more.

library(gganimate)

p_annual +
  transition_time(Year)

p_annual +
   transition_reveal(Year, along = Year)

2.8 Extra Credit) Use the data and make something wholly new and awesome. Even extra extra credit for something amazing animated.

3 Extra Credit) Go to the internet, and find a package with some cool theme you want to use in ggplot2. Use it with one of the above plots. The cooler the theme, the more points we’ll give! Note - this guy - http://byrneslab.net/project/hensel/ - is in charge of deciding how cool it is.